Problem Set 2 - Problem Set 2 Chemistry 208 Spring 2005...

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1 1. Ludwig Boltzmann theorized that the entropy of a state is related to the number of ways that state can be achieved. This is the probabilistic interpretation of entropy. The equation that describes this theory is S=k lnW. To investigate the consequences of this equation consider a double-chambered flask containing 8 atoms (see the figure below). Each atom, numbered 1 – 8, can be in either the left chamber (L) or the right chamber (R). For our purposes, there are 9 different states of the system: {8L, 0R; 7L, 1R; 6L, 2R; . . .; 0L, 8R}, where the integer denotes the number of molecules in the specified side. Importantly, each state is not unique. For example, there are 8 different ways forming the state {7L, 1R}. For this state W = 8. (a) Calculate W and S for each of the 9 different states of the system. Explain your reasoning. Express your final answer in a table. (b) Graph S as a function of number of molecules in the left chamber. (c) Suppose you cool the left-hand side of the flask down to absolute zero, which will cause all of the gas molecules to condense on the left-hand side. Does this spontaneous ordering violate the second law of thermodynamics? Explain.
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This homework help was uploaded on 04/01/2008 for the course CHEM 2080 taught by Professor Davis,f during the Spring '07 term at Cornell University (Engineering School).

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Problem Set 2 - Problem Set 2 Chemistry 208 Spring 2005...

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